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 Mat. Sb. (N.S.), 1981, Volume 116(158), Number 4(12), Pages 483–501 (Mi msb2478)

Invertibility of almost periodic $c$-continuous functional operators

V. E. Slyusarchuk

Abstract: Statements are proved about the invertibility of operators $\frac{d^m}{dt^m}+A$ ($m$ a positive integer) and $B$ acting in the space of bounded vector-valued functions on $(-\infty,\infty)$ and in the space of bounded vector-valued functions on a countable Abelian group, respectively.
Bibliography: 25 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 44:4, 431–446

Bibliographic databases:

UDC: 517.948.35
MSC: Primary 47E05; Secondary 34A10, 43A60, 46E15

Citation: V. E. Slyusarchuk, “Invertibility of almost periodic $c$-continuous functional operators”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 483–501; Math. USSR-Sb., 44:4 (1983), 431–446

Citation in format AMSBIB
\Bibitem{Sly81} \by V.~E.~Slyusarchuk \paper Invertibility of almost periodic $c$-continuous functional operators \jour Mat. Sb. (N.S.) \yr 1981 \vol 116(158) \issue 4(12) \pages 483--501 \mathnet{http://mi.mathnet.ru/msb2478} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=665850} \zmath{https://zbmath.org/?q=an:0503.34012} \transl \jour Math. USSR-Sb. \yr 1983 \vol 44 \issue 4 \pages 431--446 \crossref{https://doi.org/10.1070/SM1983v044n04ABEH000976} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. G. Kurbatov, “Invertibility of almost-periodic operators”, Funct. Anal. Appl., 19:3 (1985), 223–224
2. V. E. Slyusarchuk, “Invertibility of nonautonomous functional-differential operators”, Math. USSR-Sb., 58:1 (1987), 83–100
3. V. G. Kurbatov, “On the invertibility of almost periodic operators”, Math. USSR-Sb., 67:2 (1990), 367–377
4. Bong C., “On Some Conditions of Reversibility of C-Continuity Differential-Functional Operators”, Dokl. Akad. Nauk, 329:3 (1993), 278–280
5. A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348
6. V. E. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of the non-linear difference operator $(\mathscr Dx)(t)=x(t+1)-f(x(t))$ in the space of bounded continuous functions on the real axis”, Sb. Math., 192:4 (2001), 565–576
7. Slyusarchuk V., “Necessary and Sufficient Conditions for Existence and Uniqueness of Bounded and Almost-Periodic Solutions of Nonlinear Differential Equations”, Acta Appl. Math., 65:1-3 (2001), 333–341
8. V. E. Slyusarchuk, “Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping $d/dt-f$ in the Spaces $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$”, Math. Notes, 73:6 (2003), 843–854
9. Slyusarchuk V.Yu., “Invertibility of the Nonlinear Operator (Lx)(T) = H (X(T), Dx(T)/Dt) in the Space of Functions Bounded on the Axis”, Nonlinear Oscil., 11:3 (2008), 442–460
10. Slyusarchuk V.Yu., “Generalization of the Mukhamadiev Theorem on the Invertibility of Functional Operators in the Space of Bounded Functions”, Ukr. Math. J., 60:3 (2008), 462–480
11. V. E. Slyusarchuk, “Conditions for the invertibility of the nonlinear difference operator $(\mathscr Rx)(n)=H(x(n),x(n+1))$, $n\in\mathbb Z$, in the space of bounded number sequences”, Sb. Math., 200:2 (2009), 261–282
12. Slyusarchuk V.Yu., “Method of Local Linear Approximation in the Theory of Bounded Solutions of Nonlinear Differential Equations”, Ukr. Math. J., 61:11 (2009), 1809–1829
13. Slyusarchuk V.Yu., “Method of Local Linear Approximation in the Theory of Bounded Solutions of Nonlinear Difference Equations”, Nonlinear Oscil., 12:3 (2009), 380–391
14. Perestyuk M.O. Slyusarchuk V.Yu., “Green-Samoilenko Operator in the Theory of Invariant Sets of Nonlinear Differential Equations”, Ukr. Math. J., 61:7 (2009), 1123–1136
15. Slyusarchuk V.Yu., “Conditions for the Existence and Uniqueness of Bounded Solutions of Nonlinear Differential Equations”, Ukr. Math. J., 61:2 (2009), 320–335
16. V. E. Slyusarchuk, “The method of local linear approximation in the theory of nonlinear functional-differential equations”, Sb. Math., 201:8 (2010), 1193–1215
17. Slyusarchuk V.Yu., “Conditions for the Existence of Bounded Solutions of Nonlinear Differential and Functional Differential Equations”, Ukr. Math. J., 62:6 (2010), 970–981
18. V. E. Slyusarchuk, “Bounded and periodic solutions of nonlinear functional differential equations”, Sb. Math., 203:5 (2012), 743–767
19. Slyusarchuk V.Yu., “Method of Local Linear Approximation of Nonlinear Differential Operators by Weakly Regular Operators”, Ukr. Math. J., 63:12 (2012), 1916–1932
20. V. E. Slyusarchuk, “The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations”, Sb. Math., 205:6 (2014), 892–911
21. V. E. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of non-linear differential-difference equations”, Izv. Math., 78:6 (2014), 1232–1243
22. Slyusarchuk V.Yu., “Conditions For Almost Periodicity of Bounded Solutions of Nonlinear Differential Equations Unsolved With Respect To the Derivative”, Ukr. Math. J., 66:3 (2014), 432–442
23. V. E. Slyusarchuk, “Conditions for the Existence of Almost-Periodic Solutions of Nonlinear Difference Equations in Banach Space”, Math. Notes, 97:2 (2015), 268–274
24. Slyusarchuk V.Yu., “a Criterion For the Existence of Almost Periodic Solutions of Nonlinear Differential Equations With Impulsive Perturbation”, Ukr. Math. J., 67:6 (2015), 948–959
25. V. E. Slyusarchuk, “Almost-periodic solutions of discrete equations”, Izv. Math., 80:2 (2016), 403–416
26. V. E. Slyusarchuk, “Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$”, Sb. Math., 208:2 (2017), 255–268
27. Slyusarchuk V.Yu., “Favard-Amerio Theory For Almost Periodic Functional-Differential Equations Without Using the a"i-Classes of These Equations”, Ukr. Math. J., 69:6 (2017), 916–932
28. V. E. Slyusarchuk, “To Favard's theory for functional equations”, Siberian Math. J., 58:1 (2017), 159–168
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